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- W4307769710 abstract "We consider here the $3$-sphere $mathbf S^3$ seen as the boundary at infinity of the complex hyperbolic plane $mathbf{H}^2_{mathbf C}$. It comes equipped with a contact structure and two classes of special curves. First $mathbf R$-circles are boundaries at infinity of totally real totally geodesic subspaces and are tangent to the contact distribution. Second, $mathbf C$-circles, which are boundaries of complex totally geodesic subspaces and are transverse to the contact distribution. We define a quantitative notion, called slimness, that measures to what extent a continuous path in the sphere $mathbf S^3$ is near to be an $mathbf R$-circle. We analyze the classical foliation of the complement of an $mathbf R$-circle by arcs of $mathbf C$-circles. Next, we consider deformations of this situation where the $mathbf R$-circle becomes a slim curve. We apply these concepts to the particular case where the slim curve is the limit set of a quasi-Fuchsian subgroup of $mathrm{PU}(2,1)$. As a consequence, we describe a class of spherical CR uniformizations of certain cusped $3$-manifolds." @default.
- W4307769710 created "2022-11-05" @default.
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- W4307769710 date "2022-05-18" @default.
- W4307769710 modified "2023-09-23" @default.
- W4307769710 title "Slim curves, limit sets and spherical CR uniformisations" @default.
- W4307769710 doi "https://doi.org/10.48550/arxiv.2205.08797" @default.
- W4307769710 hasPublicationYear "2022" @default.
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